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Quantisation Errors in Digital Implementations of Fuzzy Controllers

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Digital Controller Implementation and Fragility

Part of the book series: Advances in Industrial Control ((AIC))

Abstract

Fuzzy Logic Controllers (FLCs) have proven useful in the control of complex and nonlinear processes. Unlike conventional control, which is based on a precise model of a process, fuzzy control is able to handle linguistic information in the form of IF-THEN rules. These rules usually encapsulate the experience of human operators and engineers. At present, most FLCs are implemented digitally. Microprocessors, digital signal processors (DSPs), and application specific integrated circuits (ASICs) are used to cope with real time fuzzy control. Therefore, the quantisation noise due to the finite length of digital words is to be taken into account in designing fuzzy systems. Digital implementations of FLCs involve three main types of quantisation errors: the analogue-to-digital (A/D) errors, the membership function errors, and the arithmetic errors. The consequences of these errors on the behaviour of a typical FLC are analysed and the problem of the selection of a digital format for fuzzy information is addressed.

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References

  1. Mamdani, E.H., Assilian, S. (1975) A fuzzy logic controller for a dynamic plant. Int. J. Man-Machine Std.7,1–13

    Article  MATH  Google Scholar 

  2. Kickert, W. J. M, Van Nauta LemkeH.R. (1976) Application of a fuzzy controller in a warm water plant. Automatica 12, 301–308

    Article  Google Scholar 

  3. Sugeno, M. (ed.) (1985) Industrial Applications of Fuzzy Control. Elsevier Science Publishers B. V. (North-Holland), The Netherlands

    Google Scholar 

  4. Hellendoorn, H., Palm, R (1994) Fuzzy system technologies at Siemens R&D. Fuzzy Sets Syst.63, 245–269

    Article  Google Scholar 

  5. Bonissone, P., Badami, V. et al. (1995) Industrial applications of fuzzy logic at General Electric. Proc. IEEE83, 450–465

    Article  Google Scholar 

  6. van der Wal, A. J. (1995) Application of fuzzy logic control in industry. Fuzzy Sets Syst.74, 33–41

    Article  Google Scholar 

  7. Bonissone, P., Chen, Y. et al. (1999) Hybrid soft computing systems: Industrial and commercial applications. Proc. IEEE87,1641–1667

    Article  Google Scholar 

  8. Jamshidi, M. (1994) On software and hardware applications of fuzzy logic, in Fuzzy Sets, Neural Networks and Soft Computing. Van Nostrand Reinhold, New York, 396–430

    Google Scholar 

  9. Costa, A., de Gloria, A. et al. (1995) Hardware solutions for fuzzy control. Proc. IEEE83, 422–434

    Article  Google Scholar 

  10. Kandel, A., Langholz, G. (eds.) (1998) Fuzzy Hardware: Architectures and Applications. Kluwer Academic Publishers, USA

    Google Scholar 

  11. Togai, M., Watanabe, H. (1986) Expert system on a chip: An engine for real-time approximate reasoning. IEEE Expert Syst. Mag.1, 55–62

    Google Scholar 

  12. Lim, M., Takefuji, Y. (1990) Implementing fuzzy rule-based systems on silicon chip. IEEE Expert Syst. Mag.5, 31–45

    Google Scholar 

  13. Samoladas, V., Petrou, L. (1994) Special-purpose architectures for fuzzy logic controllers. Microprocessimg and Microprogramming40, 275–289

    Article  Google Scholar 

  14. Eichfeld, H., Klimke, M. (1995) A General-purpose fuzzy inference processor. IEEE Micro15, 12–17

    Article  Google Scholar 

  15. Ascia, G., Catania, A. et al. (1996) A reconfigurable parallel architecture for fuzzy processor. Information Sciences88, 299–315

    Article  Google Scholar 

  16. Patyra, M. J., Grantner, J. L., Koster, K. (1996) Digital fuzzy logic controller: Design and implementation. IEEE Trans. Fuzzy Syst.4, 439–459

    Article  Google Scholar 

  17. del Campo, I., Callao, R., Tarela, J. M. (1998) Automatic implementation of different inference architectures for fuzzy control on PLDs. Computers and Electrical Engineering24, 113–121

    Article  Google Scholar 

  18. Ying, H., Silver, W., Buckley, J. J. (1990) Fuzzy control theory: A nonlinear case. Automatica26, 513–520

    Article  MATH  Google Scholar 

  19. Hwang, G. C., Lin, S. C. (1992) A stability approach to fuzzy control design for nonlinear systems. Fuzzy Sets Syst.48, 279–287

    Article  MathSciNet  MATH  Google Scholar 

  20. Wang, H. O., Tanaka, K., Griffin, M. F. (1996) An approach to fuzzy control of nonlinear systems: Stability and design issues. IEEE Trans. Fuzzy Syst.4, 14–23

    Article  Google Scholar 

  21. Chen, B., Tseng, C, Uang, H. (2000) MixedH2/H 00 fuzzy output feedback control design for nonlinear dynamic systems: An LMI approach. IEEE Trans. Fuzzy Syst.8, 249–265

    Article  Google Scholar 

  22. del Campo, I., Tarela, J. M. (1999) Consequences of the digitization on the performance of a fuzzy logic controller. IEEE Trans. Fuzzy Syst.7, 85–92

    Article  Google Scholar 

  23. Zadeh, L. A. (1965) Fuzzy sets. Inform. Control8, 338–353

    Article  MathSciNet  MATH  Google Scholar 

  24. Zadeh, L. A. (1968) Fuzzy algorithms. Inform. Control12, 94–102

    Article  MathSciNet  MATH  Google Scholar 

  25. Dubois, D., Prade, H. (1980) Fuzzy Sets and Systems. Theory and Applications. Academic Press, London

    MATH  Google Scholar 

  26. Klir, G., Folger, T. (1988) Fuzzy Sets, Uncertainty, and Information. Prentice Hall International, London

    Google Scholar 

  27. Zimmerman, H. (1990) Fuzzy Set Theory—and its Applications, 2nd edition. Kluwer Academic Pub., Boston

    Google Scholar 

  28. Kosko, B. (1992) Neural Networks and Fuzzy Systems. Prentice Hall, New Jersey

    MATH  Google Scholar 

  29. Pedrycz, (1989) Fuzzy control and fuzzy systems. John Wiley & Sons, Chichester

    MATH  Google Scholar 

  30. Lee, C. C. (1990) Fuzz logic in control systems: Fuzzy logic controller—Part I. IEEE Trans. Syst., Man, Cybern.20, 404–418

    Article  MATH  Google Scholar 

  31. Lee, C. C. (1990) Fuzz logic in control systems: Fuzzy logic controller—Part II. IEEE Trans. Syst., Man, Cybern.20, 419–435

    MATH  Google Scholar 

  32. TeranoT., Asai, K., Sugeno, M. (1991) Fuzzy Systems Theory and its Applications. Academic Press, London

    Google Scholar 

  33. Mendel, J. M. (1995) Fuzzy logic systems for engineering: A tutorial. Proc. IEEE83, 345–377

    Article  Google Scholar 

  34. Sugeno, M., Yasukawa, T. (1993) A Fuzzy-logic-based approach to qualitative modeling. IEEE Trans. Fuzzy Syst.1, 7–31

    Article  Google Scholar 

  35. JangJ.S., Sun, C. T., Mizutani, E. (1997) Neuro-Fuzzy and Soft Computing. A computational Approach to Learning and Machine Intelligence. Prentice Hall, USA

    Google Scholar 

  36. Hollstein, T., Halgamuge, S. K., Glesner, M. (1996) Computer-aided design of fuzzy system based on generic VHDL. IEEE Trans. Fuzzy Syst.4, 403–417

    Article  Google Scholar 

  37. SurmannH., Ungering, A. P. (1995) Fuzzy rule-based systems on general purpose processors. IEEE Micro 15, 40–48

    Article  Google Scholar 

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Authors
  1. Inés del Campo
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  2. José M. Tarela
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  3. Koldo Basterretxea
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Editor information

Editors and Affiliations

  1. Department of Electronic and Computer Engineering, Brunel University, Uxbridge, Middlesex, UB8 3PH, UK

    Robert S. H. Istepanian BSc, MSc, PhD

  2. Department of Mechanical Engineering, King’s College London, Strand, London, WC2R 2LS, UK

    James F. Whidborne MA, MSc, PhD

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© 2001 Springer-Verlag London

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del Campo, I., Tarela, J.M., Basterretxea, K. (2001). Quantisation Errors in Digital Implementations of Fuzzy Controllers. In: Istepanian, R.S.H., Whidborne, J.F. (eds) Digital Controller Implementation and Fragility. Advances in Industrial Control. Springer, London. https://doi.org/10.1007/978-1-4471-0265-6_14

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  • DOI: https://doi.org/10.1007/978-1-4471-0265-6_14

  • Publisher Name: Springer, London

  • Print ISBN: 978-1-4471-1082-8

  • Online ISBN: 978-1-4471-0265-6

  • eBook Packages: Springer Book Archive

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